Making The Following Calculations - Coursework Example

The company This paper will focus on Qantas Airlines Limited, QAN, and the rival Virgin Australia Holdings, VAH, in conducting various statistical measures. First, monthly average price of QAN stock within a period of one year will be obtained. Secondly, the standard deviation of QAN, as evaluated in excel, will be used to investigate the variability of data from the mean. Thirdly, the mean, standard deviation, and variance will be utilized to find the probability that QAN’s stock price lies between the mean and a 5% increase. The mean and standard deviation will also be used to obtain the probability that QAN’s stock’s price will drop by more than 7%. In the same line probability that QAN’s stock price will drop by more than 3% or rise by 4% will be explored. By using a confidence level of 95%, confidence interval for the stock’s price will be built. Given the current average actual price of QAN stock as 3.5328, one-sample hypothesis testing will be conducted to show whether it is reasonable to expect that the fundamental price of the stock could be 3% more than its current average. In this case, the hypothesized mean will be 3.63880 i.e. 103% of the current actual price. Finally, a two sample hypothesis test will come in handy to assess whether QAN and the rival Virgin Australia Holdings Limited have the same stock price. Company overview According to Qantas Airlines Limited (2014), Qantas started its business in 1920 in Queensland. Over the years, Qantas has grown both locally, regionally, and internationally. Originally registered as Queensland and Northern Territory Aerial Services Limited, the airline is the strongest brand in Australia and is currently classified as the global leader in long haul airline. Safety, operation reliability, engineering, maintenance, and customer service are areas that Qantas have registered excellence. The principle business conducted by Qantas is transportation of customers using Qantas and Jetstar airline brands. Besides, Qantas operates secondary businesses including subsidiaries and Q Catering. In the domestic market, Qantas Airlines Limited controls more than 62% of the domestic market. Qantas Airways Limited trades as QAN in Australia Stock Exchange. QAN had a market capitalization of AUD$8,435 billion as of the year 2015. For the fiscal year ending June 2016, QAN reported revenues of AUD$ 15,784 million compared with rival company’s revenue, VAH, of AUD$ 4,986 million. The current gross profit of QAN stands at AUD$9,172 compared with AUD$ 3,967 of VAH. The EBITDA ratio of QAN is 2,932 in comparison with 37 of VAH. In terms of efficiency, AQN has higher asset turnover of 0.92 for the fiscal year ending June 2016 compared with 0.84 of VAH. Daily prices, mean, variance, and standard deviation The analysis was conducted after accessing sample of daily stock prices of QAN from the Morningstar for a period of one year ending 18th October 2016. The sample of daily prices formed the basis of calculating the mean, variance and standard deviation. The mean, variance, and standard deviation as calculated in excel were as follows: While the arithmetic mean of 3.5328 gives the average price of QAN stock for a period of one year, the standard deviation shows the variability of the stock from the arithmetic mean (Black, 114). Variance of 0.1769 also indicates the spread of stock prices from the mean point. Based on the small value of variance, it means that the daily stock prices of QAN are not much spread out from the mean. Probability of price changes Case 1 By using stock’s return and mean, standard deviation, and variance of its price, the first case is to determine the probability that QAN stock’s price will fall between the mean of 3.5328 and a 5% increase in the mean price. The new average price after a 5% increase would be 3.709465 as shown in the excel output below. From the calculations made from historical prices, the probability that QAN stock’s price will fall between the mean of 3.5328 and a 5% increase is 0.6627 or rather 66.27%. Case 2 The second scenario is to investigate the probability that QAN stock price would drop by more than 7%. This is done by finding the 7% drop in average stock price then calculating the z-score as well as the probability of the z-score. The excel output after the calculations is availed in the table below. Based on the calculations above, the possibility that stock’s price of QAN will drop by more than 7% is 22.168%. Case 3 The third case is finding out the probability that QAN’s stock price will drop by more than 3% or rise by 4%. This will involve identification of prices that corresponds to a 3% drop and a 4% rise of the stock’s price. The next stage is to evaluate the respective z-scores and adding the probability associated with the z-scores. This is detailed in the table below. The excel results tabulated above indicates that the probability of QAN stock price dropping by 3% or rising by 4% is 0.73099. The 73.099% is a high chance of the event occurring. Confidence Interval The mean and standard deviation will be utilized in finding the 95% confidence interval for the stock’s price. It is expected that confidence interval would get large as confidence level increase i.e. from 90% to 99%. This is anticipated because the level of preciseness will tend to decline as we become more confident that the interval actually contains the population mean (Kenneth, Klimber, and Sheila, 25). In utilizing a confidence level of 95%, the confidence interval for the population parameter was deduced after obtaining descriptive statistics. The descriptive statistics is tabulated below. The conclusion is that we are 95% confident that population parameter lies within the interval . One Sample Hypothesis Testing The test is designed to determine whether the fundamental QAN stock price could be 3% more than its current average of 3.5328. This is done by first finding the 103% of the current average price. Based on the new price of 3.6388, the null hypothesis would be and our alternative would be H1: μ ≠ $3.6388. The outcome of the two-tailed test executed using excel is shown in the table below. From the excel output above, t-statistic of -4.07796 is less that critical value of 1.9691 two tailed test hence null hypothesis is rejected and we conclude that the fundamental price of QAN stock is different from 3.6388. This is confirmed from the p-value which is less than . In summary, the fundamental price of QAS stock cannot be 103% of the current average price. Two Sample Hypothesis Test The two sample hypothesis test will be used to determine whether QAN and the potential rival VAH have the same stock price. In this case, the null and alternate hypothesis is as follows: Using a level of significance of 0.05 for the two tailed test is 0.05 the excel output for the test is tabulated below. The decision rule is to reject the null hypothesis if the test statistic is less that or greater than The table above shows that the test statistic of 118.85 is greater than critical value of 1.9681 hence we reject the null hypothesis and conclude that QAN and the potential rival VAH have different stock prices. This conclusion is confirmed by the p-value which is less than significance level of 0.05. Conclusion The analysis of QAN stock price reveals the prices are not much spread out from the mean. Secondly, there is a 66.27% probability that QAN stock’s price will fall between the mean of 3.5328 and a 5% increase in the price. At the same time, the possibility that stock’s price of QAN will drop by more than 7% is only 22.168%. However, there is a higher chance i.e. 73.099% that QAN stock price will drop by 3% or rise by 4%. By considering a confidence level of 95%, the population parameter lies within the interval . The one sample hypothesis test showed that the fundamental price of QAN stock is different from 3.6388. In comparing the historical stock prices of QAN and VAH, a two-sample hypothesis led to a conclusion that the stock prices of the companies are not the same. Works Cited Black, Ken. Business Statistics: Contemporary Decision Making. John Wiley & Sons, 2009. Kenneth, Lawrence, Klimber, Ronald, and Sheila, Lawrence. Fundamentals of Forecasting Using Excel, Industrial Press Inc, 2009. Read More